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There is voluminous literature concerning the scope of topological relations that span various embedding spaces from R1 to R2, Z2 , S1 and S2 , and T2. In the case of the *1 spaces, those relations have been considered as conceptualizations of both spatial relations and temporal relations. Missing from that list are the set of digital relations that exist within Z1 , representing discretized time, discretized ordered line segments, or discretized linear features as embedding spaces. Discretized time plays an essential role in timeseries data, spatio-temporal information systems, and geo-foundation models where time is represented in layers of consecutive spatial rasters and/or spatial vector objects colloquially referred to as space–time cubes or spatio-temporal stacks. This paper explores the digital relations that exist in Z1 interpreted as a regular topological space under the digital Jordan curve model as well as a folded-over temporal interpretation of that space for use in spatio-temporal information systems and geo-foundation models. The digital Jordan curve model represents the maximum expressive power between discretized objects, making it the ideal paradigm for a decision support system model. It identifies 34 9-intersection relations in Z1 , 42 9-intersection + margin relations in Z1 , and 74 temporal relations in Z1 , utilizing the 9+-intersection, the commercial standard for spatial information systems for querying topological relations. This work creates opportunities for better spatio-temporal reasoning capacity within spatio-temporal stacks and a more direct interface with intuitive language concepts, instrumental for effective utilization of spatial tools. Three use cases are demonstrated in the discussion, representing each of the utilities of Z1 within the spatial data science community. 

Background:Minimum exam averages are an essential component to ensuring academic rigor and subsequent licensure in nursing education, yet there is scant evidence to support such practices. Method:Using a descriptive correlational design, nursing faculty at a medium-sized program in the Northeast explored the relationship between establishing a 77% (C+) minimum exam average requirement for the program and licensure exam passage rates between the 2023 cohort intervention group and the 2022 cohort control group. Results:The implementation of an exam average threshold per course produced a statistically significant effect on the National Council Licensure Examination (NCLEX-RN) pass rate (z = −3.481,p< .001) and provided support for the 77% (C+) examination threshold. Conclusion:A minimum exam average policy may relieve faculty of the moral distress associated with course failures, while also safeguarding academic rigor within the undergraduate program and promoting NCLEX-RN readiness and success. 

This learning experience helps students gain experience and proficiency with issues regarding the ethical collection and use of data. Students will gain an appreciation for the risks associated with record-level identification, where data attributes, however innocently collected, can and have been used to violate privacy and lead to discrimination against individuals and protected classes of individual 

Topological relations and direction relations represent two pieces of the qualitative spatial reasoning triumvirate. Researchers have previously attempted to use the direction relation matrix to derive a topological relation, finding that no single direction relation matrix can isolate a particular topological relation. In this paper, the technique of topological augmentation is applied to the same problem, identifying a unique topological relation in 28.6% of all topologically augmented direction relation matrices, and furthermore achieving a reduction in a further 40.4% of topologically augmented direction relation matrices when compared to their vanilla direction relation matrix counterpart. 

Social change in any society entails changes in both behaviours and institutions. We model a group-structured society in which the transmission of individual behaviour occurs in parallel with the selection of group-level institutions. We consider a cooperative behaviour that generates collective benefits for groups but does not spread between individuals on its own. Groups exhibit institutions that increase the diffusion of the behaviour within the group, but also incur a group cost. Groups adopt institutions in proportion to their fitness. Finally, the behaviour may also spread globally. We find that behaviour and institutions can be mutually reinforcing. But the model also generates behavioural source-sink dynamics when behaviour generated in institutionalized groups spreads to non-institutionalized groups and boosts their fitness. Consequently, the global diffusion of group-beneficial behaviour creates a pattern of institutional free-riding that limits the evolution of group-beneficial institutions. Our model suggests that, in a group-structured society, large-scale beneficial social change can be best achieved when the relevant behaviour and institutions remain correlated. 

Crop switching, in which farmers grow a crop that is novel to a given field, can help agricultural systems adapt to changing environmental, cultural, and market forces. Yet while regional crop production trends receive significant attention, relatively little is known about the local-scale crop switching that underlies these macrotrends. We characterized local crop-switching patterns across the United States using the US Department of Agriculture (USDA) Cropland Data Layer, an annual time series of high resolution (30 m pixel size) remote-sensed cropland data from 2008 to 2022. We found that at multiple spatial scales, crop switching was most common in sparsely cultivated landscapes and in landscapes with high crop diversity, whereas it was low in homogeneous, highly agricultural areas such as the Midwestern corn belt, suggesting a number of potential social and economic mechanisms influencing farmers’ crop choices. Crop-switching rates were high overall, occurring on more than 6% of all US cropland in the average year. Applying a framework that classified crop switches based on their temporal novelty (crop introduction versus discontinuation), spatial novelty (locally divergent versus convergent switching), and categorical novelty (transformative versus incremental switching), we found distinct spatial patterns for these three novelty dimensions, indicating a dynamic and multifaceted set of cropping changes across US farms. Collectively, these results suggest that innovation through crop switching is playing out very differently in various parts of the country, with potentially significant implications for the resilience of agricultural systems to changes in climate and other systemic trends.